# Best way to measure period of a pendulum.

1. Sep 10, 2008

### TripleB

What position should you start to time the period and why? Should you start to time the period straight away or wait, and if so for how long (how many oscillations)? If the length is fixed should you use a long or short pendulum to increase precision? If the mass is fixed should you use a large or small mass to increase precision? What are possible sources of error and how can they be reduced? A stopwatch is being used to measure the period, and the pendulum models a simple pendulum consisting of a string tied to a heavy spherical bob.

My guesses: start timing at the bottom of the swing because the bob has the largest velocity at this point and hence it will be easier to identify the time when to start/stop. You should wait for a couple of oscillations to let the pendulum 'settle'; the string may not quite be taut upon release or you may introduce some twisting which would quickly dissipate after a few oscillations. You should use as long a pendulum as possible: this increases the period which decreases the relative error in the measurement of the period and the increased length reduces the relative error in the measurement of the length. The mass should be as large as possible to make the pendulum as 'simple-like' as possible (the true period (physical pendulum) depends on the moment of inertia and the simple pendulum is an idealization). Possible sources of error: friction, rotation of bob (i.e. non-planar oscillations), non-linearity of true pendulum (i.e. sin x ~ x but not exactly). For first could use smaller oscillations and hence reduce velocity (frictional force typically proportional to velocity), for second just have to try to keep oscillations planar, and for third use smaller oscillations to make approximation more accurate. Are these correct? And what other possible solutions are there?